Oscillations in a van der Pol equation with delayed argument

We consider the van der Pol equation d2 dt2 u(t )− ε d dt u(t )+ εu2(t − r) d dt u(t − r)+ u(t ) = 0 with the delayed time r, where r and ε are real parameters, with ε > 0 small and 0 r < π/2, and prove the existence and stability of a periodic solution with period near 2π and amplitude near 2/√cos r. With these properties, this solution is unique, up to translations in time.  2002 Elsevier Science (USA). All rights reserved